Digital Signal Processing Reference
In-Depth Information
To come back to the calculation of a finite series, it is necessary to sample the
frequency axis [0,1[, for example, by using regular sampling of
M
points in this
interval:
m
⎧
⎫
⎭
[2.75]
v
∈
,0
≤ ≤
m
M
−
1
⎨
⎬
M
⎩
Figure 2.5.
Sine wave and spectral folding
m
M
Thus we have, for all values of
m
∈ {0,...,
M -
1}, by noting
X
e
(
m
)
= X
(
):
N
−
1
mk
M
xke
π
−
j
2
=
∑
()
()
Xm
[2.76]
e
k
=
0
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